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Abstract This paper introduces and evaluates a general construct for trading off accuracy and overall execution duration in classification-based machine perception problems—namely, the generalized IDK classifier cascade . The aim is to select the optimal sequence of classifiers required to minimize the expected (i.e. average) execution duration needed to achieve successful classification, subject to a constraint on quality, and optionally a latency constraint on the worst-case execution duration. An IDK classifier is a software component that attempts to categorize each input provided to it into one of a fixed set of classes, returning “I Don’t Know” (IDK) if it is unable to do so with the required level of confidence. An ensemble of several different IDK classifiers may be available for the same classification problem, offering different trade-offs between effectiveness (i.e. the probability of successful classification) and timeliness (i.e. execution duration). A model for representing such characteristics is defined, and a method is proposed for determining the values of the model parameters for a given ensemble of IDK classifiers. Optimal algorithms are developed for sequentially ordering IDK classifiers into an IDK cascade, such that the expected duration to successfully classify an input is minimized, optionally subject to a latency constraint on the worst-case overall execution duration of the IDK cascade. The entire methodology is applied to two real-world case studies. In contrast to prior work, the methodology developed in this paper caters for arbitrary dependences between the probabilities of successful classification for different IDK classifiers. Effective practical solutions are developed considering both single and multiple processors.